Samantha is taking Statistics and Psychology classes during this summer session. She received a score of 85 on her Statistics test for which the class mean was 75 with a standard deviation of 8. She received a score of 72 on her Psychology test for which the class mean was 60 with standard deviation 5. On which test did she do better relative to the rest of the class? statistics test b. psychology test c. the same d. cannot answer with given information (Ctrl) -
Samantha is taking Statistics and Psychology classes during this summer session. She received a score of 85 on her Statistics test for which the class mean was 75 with a standard deviation of 8. She received a score of 72 on her Psychology test for which the class mean was 60 with standard deviation 5. On which test did she do better relative to the rest of the class? statistics test b. psychology test c. the same d. cannot answer with given information (Ctrl) -
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Statistical Comparison of Test Scores**
Samantha is taking Statistics and Psychology classes during this summer session. She received a score of 85 on her Statistics test for which the class mean was 75 with a standard deviation of 8. She received a score of 72 on her Psychology test for which the class mean was 60 with a standard deviation of 5. On which test did she do better relative to the rest of the class?
**Possible Answers:**
- a. statistics test
- b. psychology test
- c. the same
- d. cannot answer with given information
**Explanation:**
To determine on which test Samantha performed better relative to her classmates, we need to calculate her z-scores for both tests. The z-score tells us how many standard deviations away from the mean her score is.
**For the Statistics Test:**
- Score: 85
- Mean: 75
- Standard Deviation: 8
The z-score is calculated as follows:
\[ z = \frac{(X - \mu)}{\sigma} \]
\[ z = \frac{(85 - 75)}{8} \]
\[ z = \frac{10}{8} \]
\[ z = 1.25 \]
**For the Psychology Test:**
- Score: 72
- Mean: 60
- Standard Deviation: 5
The z-score is calculated as follows:
\[ z = \frac{(X - \mu)}{\sigma} \]
\[ z = \frac{(72 - 60)}{5} \]
\[ z = \frac{12}{5} \]
\[ z = 2.4 \]
Samantha's z-score for the Psychology test (2.4) is higher than her z-score for the Statistics test (1.25), indicating that she performed better on the Psychology test relative to the rest of the class.
Thus, the correct answer is:
- b. psychology test](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f54fed8-fa4e-41a3-be1d-05f34a1734d9%2F69b799a7-3107-42d4-abfa-7111313391ab%2Fzy1meqh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Statistical Comparison of Test Scores**
Samantha is taking Statistics and Psychology classes during this summer session. She received a score of 85 on her Statistics test for which the class mean was 75 with a standard deviation of 8. She received a score of 72 on her Psychology test for which the class mean was 60 with a standard deviation of 5. On which test did she do better relative to the rest of the class?
**Possible Answers:**
- a. statistics test
- b. psychology test
- c. the same
- d. cannot answer with given information
**Explanation:**
To determine on which test Samantha performed better relative to her classmates, we need to calculate her z-scores for both tests. The z-score tells us how many standard deviations away from the mean her score is.
**For the Statistics Test:**
- Score: 85
- Mean: 75
- Standard Deviation: 8
The z-score is calculated as follows:
\[ z = \frac{(X - \mu)}{\sigma} \]
\[ z = \frac{(85 - 75)}{8} \]
\[ z = \frac{10}{8} \]
\[ z = 1.25 \]
**For the Psychology Test:**
- Score: 72
- Mean: 60
- Standard Deviation: 5
The z-score is calculated as follows:
\[ z = \frac{(X - \mu)}{\sigma} \]
\[ z = \frac{(72 - 60)}{5} \]
\[ z = \frac{12}{5} \]
\[ z = 2.4 \]
Samantha's z-score for the Psychology test (2.4) is higher than her z-score for the Statistics test (1.25), indicating that she performed better on the Psychology test relative to the rest of the class.
Thus, the correct answer is:
- b. psychology test
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman